White Paper
FINAL REPORT - Part 2
Prepared by:
Dr. Thomas J. Gieseke
NUWCDIVNPT - Code 8233
March 29, 1999
The two focal points of this study were measurement of pressure loss through the Westfall Mixer and measurement of the flow-field in the wake of the Westfall Mixer.
The pressure loss measurements agreed very well with those previously published. The measured value was 13.6 based on the average flow velocity and pipe diameter. To assess how reasonable this result is, the mixer can be considered in comparison to a sharp edged orifice with a similar area reduction. The observed pressure loss is consistent with that expected from a sharp-edged orifice with a 60% reduction in area.
In application of the Westfall mixer, unmixed fluid will approach from upstream and be forced through the mixer restriction to form a high speed flow. Additive will be injected into the low-speed reversed flow region downstream of the mixer tabs. It is the way in which the low speed fully mixed fluid and the high speed unmixed interact and mix which drives the mixer performance. The velocity field measurements provided wealth of information regarding the underlying fluid mechanics associated with the Westfall mixer performance. Three velocity component statistics have been selected for presentation and discussion, the mean streamwise component, fluctuations in the streamwise component and fluctuations in the vertical component.
The dominant feature in the Westfall mixer is the production of two very strong streamwise jets emanating from the open areas in the cut-out plate. Velocities in the cores of these jets reach five times that of the mean upstream pipe flow. Large reverse flow regions surround these jets and very high amplitude shear layers exist in between the jets and the reversed flow. The effective area where high shear layers exist is largely due to the dual jet structure and the non-circular nature of the plate cut-outs.
The association of high turbulence intensity with regions of high shear can be seen through inspection of the mean and fluctuation velocity contours. Peaks in the turbulence intensity occur where rapid changes in the mean velocities are found. Reynolds stresses are the correlation between fluctuating velocity components. When the vertical and streamwise velocity components are simultaneously high, a positive combination to the Reynolds stress occurs. High Reynolds stresses are associated with high transport of momentum, temperature, and passive scalars. Because Reynolds stress is well correlated with velocity fluctuation amplitude, transport across the shear layer will also be high in these regions. Consequently, contours of fluctuating velocity can be interpreted as contours of mixing effectiveness, with the greatest mixing occurring where the turbulence intensity is the highest. The Westfall mixer effectively speeds mixing by increasing the contact area between high speed fluid and low speed fluid.
Because the tabs in the Westfall mixer are slightly swept back in the direction of the mean flow, the jets emerge at an angle with respect to the flow axis toward the walls of the pipe. The mean velocity contours track the core of the jet as it grows closer and closer to the pipe wall, eventually being contorted into a very thin layer near the wall. This contortion of the jet shape further enhances the mixer performance because the jet surface area increases drastically.
The core velocity of the jet decays slowly over the first pipe diameter downstream of the mixer. In this region the jet behaves roughly as if it were in a free field. However, once the jet has been drastically changed in shape by the presence of the wall, the core velocity drops dramatically. Between 1.0 and 2.67 diameters downstream of the mixer the core velocity drops by a factor of 2. This drop in velocity is tied to the increase in surface area of the jet and the associated increase of momentum transport between the jet and the low speed fluid. As previously noted, momentum and scalar transport are very well correlated. The change in jet geometry due to its interaction with the pipe walls enables an exchange of transported properties between the jet and the low speed fluid to take place rapidly. The rapid rise in the fluctuating velocity components in this region is further evidence of enhanced mixing due to the walls.
There has been discussion that an important hydrodynamics mechanism contributing to the Westfall mixer operation is the action of large streamwise eddies. Owing to the very high fluctuations in streamwise and vertical velocities as compared to the mean vertical velocity component, the transport associated with bulk fluid motion is small compared to the influence of turbulence. In addition, review of flow visualization and unreported test data support the assertion that these eddies do not significantly contribute to the mixer effectiveness.
An unusual feature was observed in the streamwise development of velocity fluctuations. The amplitude of fluctuation initially rises with distance downstream of the mixer. It is likely that the increased interaction of the jet with the pipe walls causes the turbulence intensity to rise.
In addition to the turbulence measured within the mixer, there is another significant source of unsteadiness with the device. The two jets formed by the mixer and the recirculating zones behind the tabs do not exist together in a stable pattern. Based on flow visualization and observation of the instantaneous velocity signals, it was observed that the flow slowly oscillates from preferring a large circulation behind one tab and then to preferring a circulation behind the other. Measurements of spectra did not show any identifiable periodicity to this behavior but it was clearly observed when dye was injected into the mixer and observed. It was also observed in the velocity signal time traces. The mean velocities at any given point slowly oscillated (1 second or longer period) over a wide range, indicating a bi-stable flow. The impact on mixing is unknown. It is likely that the increased interaction of the jets with the walls improves mixing.
A sensitivity test was conducted by injecting dye into the pipe at a range of locations aft of the mixer. The disturbance caused by the injection of dye caused the flow to switch to a state where circulation behind one of the tabs dominated (opposite the point of injection). Which circulation zone dominated the flow was a function of how the dye was injected.
The Westfall mixer functions well because it makes effective use of shear layers. Transport of momentum, energy, and passive scalars across these shear layers is determined by the area of, the velocity ratio across, and the turbulence intensity in the shear layers. The Westfall mixer design has effectively enhanced these quantities by using a unique orifice plate design and interactions of the flow with the pipe walls